Spokespeople for Hatch and the White House didn't immediately respond to a request for comment.

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But Cornyn appeared skeptical that a separate working group was needed, signaling it would be redundant with the role of the Finance Committee, which is taking the lead on tax reform in the Senate.

"That's what we do as a committee. So I don't really personally see the benefit of creating additional structure," he said.

Trump's suggestion — made during a White House meeting with members of the Senate panel — comes as Republicans are expected to pass a budget this week that will allow them to avoid a Democratic filibuster on tax reform.

Republicans released a framework for their tax plan late last month and would like to pass a bill by the end of the year, hopeful it will give them a needed win on an important agenda item as they head into 2018.

The White House is trying to win over at least one Democratic senator, largely focusing their efforts on a coalition of red-state lawmakers up for reelection next year in states Trump won in 2016.

Republicans have a narrow path to clearing a tax plan if they can't win over a Democratic senator.

With a 52-seat majority, they would need 50 GOP senators to support the plan in order to let Vice President Pence break a tie in the Senate. There are already signs they could struggle to unite the caucus behind their framework.

But some of those Democrats said after the White House meeting that they remain unconvinced.

Cornyn added on Monday that lawmakers already have "all the tools we need in order to come up with a consensus bill if Democrats will participate."

"As I tried to explain we're going to have a mark up and a bipartisan opportunity to amend the bill, and you might win some votes, you might lose some votes, but that's the way the legislation normally functions," he said.

Republicans came under fire from Democrats and some members of their own party for not having a markup or public hearing on their push to repeal and replace ObamaCare before votes in late July.

GOP leadership in turn said their tax-reform effort would go through the committee process, which will include public hearings and the chance for Democrats to offer amendments to change the bill.